Cracks Interaction Effect on the Dynamic Stability of Beams under Conservative and Nonconservative Forces
This study is an extension of the paper by E. Viola and A. Marzani  where the eigenfrequencies and critical loads of a single cracked beam subjected to conservative and nonconservative forceshave been investigated. Here the aim is to analyze the dynamic stability of T cross section beams withmultiple cracks. A doubly cracked Euler-Bernoulli beam subjected to triangularly distributed subtangential forces, which are the combination of axial and tangential forces, is considered. The governingequation of the system is derived via the extended Hamilton’s principle in which the kinetic energy, theelastic potential energy, the conservative work and the nonconservative work are taken into account. Thelocal ﬂexibility matrix for a beam with T cross-section is used to model the cracked section. The resultsshow that for given boundary conditions cracked beams become unstable in the form of either ﬂutter ordivergence depending on the crack parameters, the nonconservativeness of the applied load as well as theinteraction of the two cracks.
Z. Tonković and M.H. Aliabadi
E. Viola et al., "Cracks Interaction Effect on the Dynamic Stability of Beams under Conservative and Nonconservative Forces", Key Engineering Materials, Vols. 488-489, pp. 383-386, 2012